Are Accelerated and Enhanced Wave Function Methods Accurate to Compute Static Linear and Nonlinear Optical Properties?

Assessment of RPA and σ-functional methods for the calculation of dipole moments and static polarizabilities and hyperpolarizabilities

In the present paper, we assess the performance of methods based on the random phase approximation (RPA) and on σ-functionals for predicting static optical properties, i.e., dipole moment, polarizability, and first and second hyperpolarizability, of small- and medium-sized molecules, including chain-like systems. First, we provide accurate reference data by coupled-cluster singles, doubles, with perturbative triples calculations with sufficiently large basis sets. The RPA and σ-functional calculations are carried out post-self-consistently using input orbitals and eigenvalues from the hybrid density-functional calculation. The optimal fraction of exact non-local exchange in these calculations is found to be quite high, around 0.5-0.6 in RPA and around 0.8-1.0 in σ-functional methods. σ-functional methods, however, proved to be less sensitive than RPA methods with respect to the amount of exact non-local exchange used in the generation of their input data. σ-functional methods are shown to outperform in accuracy RPA methods and various other considered density-functional theory methods for static optical properties and, thus, are well-suited for the calculation of linear and non-linear optical properties.

Toward a realistic theoretical electronic spectra of metal aqua ions in solution: The case of Ce(H2O)n3+ using statistical methods and quantum chemistry calculations

Accurately predicting spectra for heavy elements, often open-shell systems, is a significant challenge typically addressed using a single cluster approach with a fixed coordination number. Developing a realistic model that accounts for temperature effects, variable coordination numbers, and interprets experimental data is even more demanding due to the strong solute-solvent interactions present in solutions of heavy metal cations. This study addresses these challenges by combining multiple methodologies to accurately predict realistic spectra for highly charged metal cations in aqueous media, with a focus on the electronic absorption spectrum of Ce3+ in water. Utilizing highly correlated relativistic quantum mechanical (QM) wavefunctions and structures from molecular dynamics (MD) simulations, we show that the convolution of individual vertical transitions yields excellent agreement with experimental results without the introduction of empirical broadening. Good results are obtained for both the normalized spectrum and that of absolute intensity. The study incorporates a statistical machine learning algorithm, Gaussian Mixture Models-Nuclear Ensemble Approach (GMM-NEA), to convolute individual spectra. The microscopic distribution provided by MD simulations allows us to examine the contributions of the octa- and ennea-hydrate of Ce3+ in water to the final spectrum. In addition, the temperature dependence of the spectrum is theoretically captured by observing the changing population of these hydrate forms with temperature. We also explore an alternative method for obtaining statistically representative structures in a less demanding manner than MD simulations, derived from QM Wigner distributions. The combination of Wigner-sampling and GMM-NEA broadening shows promise for wide application in spectroscopic analysis and predictions, offering a computationally efficient alternative to traditional methods.

State-of-the-art local correlation methods enable affordable gold standard quantum chemistry for up to hundreds of atoms

In this feature, we review the current capabilities of local electron correlation methods up to the coupled cluster model with single, double, and perturbative triple excitations [CCSD(T)], which is a gold standard in quantum chemistry. The main computational aspects of the local method types are assessed from the perspective of applications, but the focus is kept on how to achieve chemical accuracy (i.e., <1 kcal mol-1 uncertainty), as well as on the broad scope of chemical problems made accessible. The performance of state-of-the-art methods is also compared, including the most employed DLPNO and, in particular, our local natural orbital (LNO) CCSD(T) approach. The high accuracy and efficiency of the LNO method makes chemically accurate CCSD(T) computations accessible for molecules of hundreds of atoms with resources affordable to a broad computational community (days on a single CPU and 10-100 GB of memory). Recent developments in LNO-CCSD(T) enable systematic convergence and robust error estimates even for systems of complicated electronic structure or larger size (up to 1000 atoms). The predictive power of current local CCSD(T) methods, usually at about 1-2 order of magnitude higher cost than hybrid density functional theory (DFT), has become outstanding on the palette of computational chemistry applicable for molecules of practical interest. We also review more than 50 LNO-based and other advanced local-CCSD(T) applications for realistic, large systems across molecular interactions as well as main group, transition metal, bio-, and surface chemistry. The examples show that properly executed local-CCSD(T) can contribute to binding, reaction equilibrium, rate constants, etc. which are able to match measurements within the error estimates. These applications demonstrate that modern, open-access, and broadly affordable local methods, such as LNO-CCSD(T), already enable predictive computations and atomistic insight for complicated, real-life molecular processes in realistic environments.

On the third-order nonlinear optical responses of cis and trans stilbenes - a quantum chemistry investigation

The second hyperpolarizabilities (γ) of the stilbene molecular switch in its trans and cis forms have been calculated using quantum chemistry methods to address their third-order nonlinear optical contrasts, to assess the reliability of lower-cost DFT methods, and to make comparisons with experiments. First, the reference CCSD(T) method shows that trans-stilbene presents a γ‖ value twice larger than its cis isomer (its γTHS value is 2.7 times larger). Among more cost-effective methods, reliable results are obtained at MP2 as well as with DFT, provided the CAM-B3LYP or ωB97X-D XCFs are employed. Supplementary DFT calculations have investigated the relationships between the accuracy of the exchange-correlation functionals, the fulfillment of Koopmans' theorem, and the delocalization error, and they demonstrated that satisfying Koopmans' theorem is not the condition for the best accuracy but that functionals with small delocalization errors are generally efficient. Using the selected CAM-B3LYP, large γ enhancements by about 70% (trans-stilbene) and 50% (cis-stilbene) have been evidenced when accounting for solvent effects using an implicit solvation model (IEFPCM), even for apolar solvents. Then, the frequency dispersion of the γ responses has been described using Bishop polynomial expansions, allowing comparisons with a broad set of experimental data. To a certain extent, no systematic agreement between the calculations and the measured values was found. On the one hand, the agreement is satisfactory for the γ(-ω;ω,-ω,ω) quantities, provided that the dominant vibrational contribution is taken into account. On the other hand, the agreement is poor for the γ(-2ω;ω,ω,0) and γ(-3ω;ω,ω,ω) quantities, while some inconsistencies between experimental values are also highlighted.

Application to nonlinear optical properties of the RSX-QIDH double-hybrid range-separated functional

The effective calculation of static nonlinear optical properties requires a considerably high accuracy at a reasonable computational cost, to tackle challenging organic and inorganic systems acting as precursors and/or active layers of materials in (nano-)devices. That trade-off implies to obtain very accurate electronic energies in the presence of externally applied electric fields to consequently obtain static polarizabilities (α i j ) and hyper-polarizabilities (β i j k andγ i j k l ). Density functional theory is known to provide an excellent compromise between accuracy and computational cost, which is however largely impeded for these properties without introducing range-separation techniques. We thus explore here the ability of a modern (double-hybrid and range-separated) Range-Separated eXchange Quadratic Integrand Double-Hybrid exchange-correlation functional to compete in accuracy with more costly and/or tuned methods, thanks to its robust and parameter-free nature.

Accurate and Efficient Prediction of Post-Hartree-Fock Polarizabilities of Condensed-Phase Systems

To accurately and efficiently predict the molecular response properties (such as polarizability) at post-Hartree-Fock levels for condensed-phase systems under periodic boundary conditions (PBC) is still an unaccomplished and ongoing task. We demonstrate that static isotropic polarizabilities can be cost-effectively predicted at post-Hartree-Fock levels by combining the linear-scaling generalized energy-based fragmentation (GEBF) and information-theoretic approach (ITA) quantities. In PBC-GEBF, the total molecular polarizability of an extended system is obtained as a linear combination of the corresponding quantities of a series of small embedded subsystems of several monomers. Here, we show that in the PBC-GEBF-ITA framework, one can obtain the molecular polarizabilities and establish linear relations to ITA quantities. Once these relations are established for smaller subsystems, one can predict the polarizabilities of larger subsystems directly from the molecular wavefunction (or electron density) via ITA quantities. Alternatively, one can determine the total molecular polarizability via a linear combination equation in PBC-GEBF. We have corroborated that this newly proposed PBC-GEBF-ITA protocol is much more efficient than the original PBC-GEBF approach but is not much less accurate and that this conclusion holds for both many-body perturbation theory and the coupled cluster calculations. Good efficiency and transferability of the PBC-GEBF-ITA protocol are demonstrated for periodic systems with several hundred atoms in a unit cell.

RPA, an Accurate and Fast Method for the Computation of Static Nonlinear Optical Properties

The accurate computation of static nonlinear optical properties (SNLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic connection fluctuation theorem is known to be a reliable and cost-effective method to render electronic correlation effects when combined with density-fitting techniques and integration over imaginary frequencies. We explore the ability of the RPA energy expression to predict SNLOPs by evaluating RPA electronic energies in the presence of finite electric fields to obtain (using the finite difference method) static polarizabilities and hyperpolarizabilities. We show that the RPA based on hybrid functional self-consistent field calculations yields accurate SNLOPs as the best-tuned double-hybrid functionals developed today, with the additional advantage that the RPA avoids any system-specific adjustment.